Vận dụng kiến thức giải Giải bài 49 trang 42 sách bài tập Toán 6 – Cánh Diều Tập 2 – Bài 4. Phép nhân – phép chia phân số. Tìm x biết:…
Đề bài/câu hỏi:
Tìm x biết:
a) \(\frac{6}{7}.\,x = \frac{{18}}{{23}}\)
b) \(\frac{{15}}{{119}}.\,x = 1\)
c) \(x:\frac{5}{6} = \frac{4}{7}\)
d) \(x – \frac{3}{7}:\frac{9}{{14}} = \frac{{ – 7}}{3}\)
e) \(\frac{9}{{13}}.\,x = \frac{{11}}{8} – \frac{{125}}{{1000}}\)
g) \(\left( {x – \frac{1}{2}} \right):\frac{3}{{11}} = \frac{{11}}{4}\)
Lời giải:
a) \(\frac{6}{7}.\,x = \frac{{18}}{{23}} \Rightarrow x = \frac{{18}}{{23}}:\frac{6}{7} \Rightarrow x = \frac{{18}}{{23}}.\frac{7}{6} = \frac{{18.7}}{{23.6}} = \frac{{21}}{{23}}\)
b) \(\frac{{15}}{{119}}.\,x = 1 \Rightarrow x = 1:\frac{{15}}{{119}} \Rightarrow x = \frac{{119}}{{15}}\)
c) \(x:\frac{5}{6} = \frac{4}{7} \Rightarrow x = \frac{5}{6}.\frac{4}{7} = \frac{{5.4}}{{6.7}} = \frac{{10}}{{21}}\)
d)
\(\begin{array}{l}x – \frac{3}{7}:\frac{9}{{14}} = \frac{{ – 7}}{3} \Rightarrow x – \frac{3}{7}.\frac{{14}}{9} = \frac{{ – 7}}{3}\\ \Rightarrow x – \frac{2}{3} = \frac{{ – 7}}{3} \Rightarrow x = \frac{2}{3} + \frac{{ – 7}}{3} = \frac{{ – 5}}{3}\end{array}\)
e)
\(\begin{array}{l}\frac{9}{{13}}.\,x = \frac{{11}}{8} – \frac{{125}}{{1000}} \Rightarrow \frac{9}{{13}}.\,x = \frac{{11}}{8} – \frac{1}{8} \Rightarrow \frac{9}{{13}}.\,x = \frac{{10}}{8}\\ \Rightarrow \frac{9}{{13}}.\,x = \frac{5}{4} \Rightarrow x = \frac{5}{4}:\frac{9}{{13}} \Rightarrow x = \frac{5}{4}.\frac{{13}}{9} = \frac{{5.13}}{{4.9}} = \frac{{65}}{{36}}\end{array}\)
g)
\(\begin{array}{l}\left( {x – \frac{1}{2}} \right):\frac{3}{{11}} = \frac{{11}}{4} \Rightarrow x – \frac{1}{2} = \frac{{11}}{4}.\frac{3}{{11}}\\ \Rightarrow x – \frac{1}{2} = \frac{3}{4} \Rightarrow x = \frac{1}{2} + \frac{3}{4} = \frac{2}{4} + \frac{3}{4} = \frac{5}{4}\end{array}\)